Table 4. Tests for Longitudinal Invariance, PHQ Item Subsets^a.

Model Description	Family n	Patient n	P for χ2 test of fit
PHQ-2:
Items #1, 2	125	88	0.342
Other 2-indicator models:
Items #2, 4	124	87	0.392
Items #2, 3	124	87	0.321
Items #2, 7	124	87	0.296
Items #1, 5	124	89	0.078
Items #2, 5	123	87	0.078
Items #1, 3	125	89	0.059
3-indicator models:
Items #2, 7, 8	124	87	0.255
Items #2, 3, 8	122	86	0.245
Items #2, 3, 5	122	87	0.242
Items #2, 4, 8	122	86	0.235
Items #1, 2, 8	123	87	0.170
Items #1, 5, 8	121	87	0.169
Items #2, 5, 8	121	86	0.158
Items #2, 3, 4	122	86	0.125
Items #1, 4, 8	122	87	0.122
Items #1, 3, 8	122	87	0.119
Items #1, 2, 4	123	87	0.110
Items #2, 4, 7	122	86	0.096
Items #1, 7, 8	124	88	0.092
Items #1, 3, 5	123	89	0.064
4-indicator models:
Items #1, 2, 4, 8	121	86	0.151
Items #1, 4, 5, 8	120	86	0.147
Items #1, 2, 5, 8	120	86	0.146
Items #2, 4, 7, 8	122	86	0.139
Items #1, 3, 5, 8	120	87	0.138
Items #2, 4, 5, 8	120	85	0.117
Items #2, 3, 7, 8	122	86	0.112
Items #1, 5, 7, 8	121	87	0.077
Items #2, 3, 4, 5	121	86	0.054
Items #1, 3, 4, 8	120	86	0.050
5-indicator models:
Items #1, 2, 4, 5, 8	119	85	0.117
Items #2, 3, 5, 7, 8	120	86	0.071
Items #1, 3, 4, 5, 8	119	86	0.063

^aTable shows all item combinations that were theoretically tenable as models of depression (because they included the anhedonia and/or depressed mood indicator) and for which the test for longitudinal invariance produced χ² probability >0.05 and “proper” estimates (i.e., positive definite theta and psi matrices); three models were excluded solely because they produced improper estimates. The following models had χ² probability >0.05 and proper estimates, but did not include anhedonia or depressed mood, and were, therefore, excluded from the table: items 3-4, 3-5, 3-8; 3-4-8, 3-5-8, 4-5-8, 5-7-8; 3-4-5-8; three additional models that excluded anhedonia or depressed mood were excluded because they also produced improper estimates.